Quantitative models play a central role in understanding the impact of adaptive processes on shaping patterns of standing genetic variation (the number and frequencies of mutations in natural populations, with special regard to those contributing to heritable variation in traits. Understanding how observations on patterns of such variation relate to models helps us design and interpret genetic association studies intended to map mutations underlying this heritable variation. This project will integrate two historically separate areas of theoretical genetics into a common simulation framework in order to study the dynamics of the adaptive evolution of complex traits (those affected by multiple genes and environmental influences) in order to understand the implications of such models for the interpretation of population genomic data and the design of association studies. The broader relevance of the research is related to association studies, which attempt to map mutations leading to traits like the risk of heritable disease.